If x(0)= 1/2, between 0 and 6, then three of the factors, x, x, and (x+ 10) are positive while the fourth, x- 6, is negative. That means that the solution is decreasing- and, as long as it stays between 0 and 6, is always decreasing. Since the solution curve cannot cross x= 0 (because of uniqueness) this solution will go to 0 as x-> infinity.

If x(0)= 1/2, between 0 and 6, then three of the factors, x, x, and (x+ 10) are positive while the fourth, x- 6, is negative. That means that the solution is decreasing- and, as long as it stays between 0 and 6, is always decreasing. Since the solution curve cannot cross x= 0 (because of uniqueness) this solution will go to 0 as x-> infinity.